Question

If $\sin \theta +\cos \theta =\sqrt{2}\cos ({90}^{\circ }-\theta )$, find $\cot \theta$ ?

Answer 1

Given:

$\sin \theta +\cos \theta =\sqrt{2}\cos (90-\theta )$

$\Rightarrow \sin \theta +\cos \theta =\sqrt{2}\sin \theta$ [$\because \cos ({90}^{\circ }-\theta )=\sin \theta$]

$\Rightarrow (1-\sqrt{2})\sin \theta =\cos \theta$

$\Rightarrow \frac{\cos \theta }{\sin \theta }=1-\sqrt{2}$

$\therefore \cot \theta =1-\sqrt{2}$ [ $\because \frac{\cos \theta }{\sin \theta }=\cot \theta$]